Hilbert functions in computational algebraic geometry

The problem of finding the smallest degree from which the Hilbert function equals the Hilbert polynomial is central in solving polynomial equations. In this talk, I will justify this claim and illustrate it for symmetric tensor decomposition, and for solving equations on Grassmannians and del Pezzo surfaces.

This is joint work with Barbara Betti, Fulvio Gesmundo, Leonie Kayser and Marta Panizzut.